Question

Find the value of x. Round the length to the nearest tenth. The diagram is not drawn to scale.

Answer 1

For the given triangle, the value of x is 2,880.2 m.

Step-by-step explanation:

Step 1:

The sum of the angles on a straight line is 90°. It is given that the sum of the upper sides angle and 10° is 90°.

So the triangle has an angle of 80° on the top side.

Step 2:

For the top side, the hypotenuse measures x m and the adjacent side measures 500 m.

To determine the value of x, we determine the cos of the given angle.

$cos \theta = \frac{adjacentside}{hypotenuse} , cos 80 = 0.1736, cos 80 = \frac{500}{x}.$

$x = (500)(0.1736) = 2,880.1843.$

So rounding this off, we get the value of x is 2,880.2 m.